detailed information: The input equation set is:
 | | | | -20 | x | + | | 61 | y | + | | | 1 2 | z | = | | 91 | | (2) |
| | Question solving process:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 20 | x | | -10 | y | | - | 1 4 | z | = | | - | 7 2 | (4) | , then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
Divide the two sides of equation (1) by 2, the equation can be obtained: | | 20 | x | | -10 | y | | - | 1 4 | z | = | | - | 7 2 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
Multiply both sides of equation (2) by 10 Divide the two sides of equation (2) by 51, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 | | | | | - | 163 204 | z | = | | - | 1393 102 | | (3) |
|
Multiply both sides of equation (3) by 51 Divide both sides of equation (3) by 163, get the equation: | - | 163 652 | z | = | | - | 1393 326 | (7) | , then add the two sides of equation (7) to both sides of equation (2), get the equation:
 | | | | | - | 163 204 | z | = | | - | 1393 102 | | (3) |
|
Multiply both sides of equation (3) by 102 Divide both sides of equation (3) by 163, get the equation: | - | 163 326 | z | = | | - | 1393 163 | (8) | , then subtract both sides of equation (8) from both sides of equation (1), get the equation:
 | | | | | - | 163 204 | z | = | | - | 1393 102 | | (3) |
|
Multiply both sides of equation (2) by 20 Divide both sides of equation (2) by 51, get the equation:, then add the two sides of equation (9) to both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |